TSTP Solution File: PLA054^4 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : PLA054^4 : TPTP v8.2.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 02:21:20 EDT 2024
% Result : Theorem 0.22s 0.41s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PLA054^4 : TPTP v8.2.0. Released v8.1.0.
% 0.07/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat May 18 13:40:23 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a TH0_THM_EQU_NAR problem
% 0.14/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.38 % (3080)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.38 % (3080)Instruction limit reached!
% 0.14/0.38 % (3080)------------------------------
% 0.14/0.38 % (3080)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (3080)Termination reason: Unknown
% 0.14/0.38 % (3080)Termination phase: Property scanning
% 0.14/0.38
% 0.14/0.38 % (3080)Memory used [KB]: 1023
% 0.14/0.38 % (3080)Time elapsed: 0.003 s
% 0.14/0.38 % (3080)Instructions burned: 3 (million)
% 0.14/0.38 % (3080)------------------------------
% 0.14/0.38 % (3080)------------------------------
% 0.14/0.38 % (3074)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.14/0.38 % (3075)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.14/0.38 % (3076)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.38 % (3073)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.38 % (3077)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.38 % (3078)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.14/0.38 % (3079)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.38 % (3076)Instruction limit reached!
% 0.14/0.38 % (3076)------------------------------
% 0.14/0.38 % (3076)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (3076)Termination reason: Unknown
% 0.14/0.38 % (3077)Instruction limit reached!
% 0.14/0.38 % (3077)------------------------------
% 0.14/0.38 % (3077)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (3076)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (3076)Memory used [KB]: 1023
% 0.14/0.38 % (3076)Time elapsed: 0.003 s
% 0.14/0.38 % (3076)Instructions burned: 2 (million)
% 0.14/0.38 % (3076)------------------------------
% 0.14/0.38 % (3076)------------------------------
% 0.14/0.38 % (3077)Termination reason: Unknown
% 0.14/0.38 % (3077)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (3077)Memory used [KB]: 1023
% 0.14/0.38 % (3077)Time elapsed: 0.003 s
% 0.14/0.38 % (3077)Instructions burned: 2 (million)
% 0.14/0.38 % (3077)------------------------------
% 0.14/0.38 % (3077)------------------------------
% 0.14/0.38 % (3074)Instruction limit reached!
% 0.14/0.38 % (3074)------------------------------
% 0.14/0.38 % (3074)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (3074)Termination reason: Unknown
% 0.14/0.38 % (3074)Termination phase: Property scanning
% 0.14/0.38
% 0.14/0.38 % (3074)Memory used [KB]: 1023
% 0.14/0.38 % (3074)Time elapsed: 0.004 s
% 0.14/0.38 % (3074)Instructions burned: 4 (million)
% 0.14/0.38 % (3074)------------------------------
% 0.14/0.38 % (3074)------------------------------
% 0.14/0.38 % (3078)Refutation not found, incomplete strategy
% 0.14/0.38 % (3078)------------------------------
% 0.14/0.38 % (3078)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (3078)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.38
% 0.14/0.38
% 0.14/0.38 % (3078)Memory used [KB]: 5500
% 0.14/0.38 % (3078)Time elapsed: 0.005 s
% 0.14/0.38 % (3078)Instructions burned: 5 (million)
% 0.14/0.38 % (3078)------------------------------
% 0.14/0.38 % (3078)------------------------------
% 0.14/0.39 % (3079)Instruction limit reached!
% 0.14/0.39 % (3079)------------------------------
% 0.14/0.39 % (3079)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (3079)Termination reason: Unknown
% 0.14/0.39 % (3079)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (3079)Memory used [KB]: 5628
% 0.14/0.39 % (3079)Time elapsed: 0.012 s
% 0.14/0.39 % (3079)Instructions burned: 19 (million)
% 0.14/0.39 % (3079)------------------------------
% 0.14/0.39 % (3079)------------------------------
% 0.14/0.39 % (3081)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.14/0.39 % (3082)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.14/0.40 % (3083)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.40 % (3075)Instruction limit reached!
% 0.14/0.40 % (3075)------------------------------
% 0.14/0.40 % (3075)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (3075)Termination reason: Unknown
% 0.14/0.40 % (3075)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (3075)Memory used [KB]: 5756
% 0.14/0.40 % (3075)Time elapsed: 0.018 s
% 0.14/0.40 % (3075)Instructions burned: 27 (million)
% 0.14/0.40 % (3075)------------------------------
% 0.14/0.40 % (3075)------------------------------
% 0.14/0.40 % (3083)Instruction limit reached!
% 0.14/0.40 % (3083)------------------------------
% 0.14/0.40 % (3083)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (3083)Termination reason: Unknown
% 0.14/0.40 % (3083)Termination phase: shuffling
% 0.14/0.40
% 0.14/0.40 % (3083)Memory used [KB]: 1023
% 0.14/0.40 % (3083)Time elapsed: 0.003 s
% 0.14/0.40 % (3083)Instructions burned: 3 (million)
% 0.14/0.40 % (3083)------------------------------
% 0.14/0.40 % (3083)------------------------------
% 0.22/0.40 % (3085)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.22/0.40 % (3084)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.22/0.40 % (3085)Instruction limit reached!
% 0.22/0.40 % (3085)------------------------------
% 0.22/0.40 % (3085)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (3085)Termination reason: Unknown
% 0.22/0.40 % (3085)Termination phase: Property scanning
% 0.22/0.40
% 0.22/0.40 % (3085)Memory used [KB]: 1023
% 0.22/0.40 % (3085)Time elapsed: 0.005 s
% 0.22/0.40 % (3085)Instructions burned: 7 (million)
% 0.22/0.40 % (3085)------------------------------
% 0.22/0.40 % (3085)------------------------------
% 0.22/0.40 % (3073)First to succeed.
% 0.22/0.40 % (3082)Instruction limit reached!
% 0.22/0.40 % (3082)------------------------------
% 0.22/0.40 % (3082)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (3082)Termination reason: Unknown
% 0.22/0.40 % (3082)Termination phase: Saturation
% 0.22/0.40
% 0.22/0.40 % (3082)Memory used [KB]: 5756
% 0.22/0.40 % (3082)Time elapsed: 0.010 s
% 0.22/0.40 % (3082)Instructions burned: 15 (million)
% 0.22/0.40 % (3082)------------------------------
% 0.22/0.40 % (3082)------------------------------
% 0.22/0.40 % (3086)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.22/0.41 % (3073)Refutation found. Thanks to Tanya!
% 0.22/0.41 % SZS status Theorem for theBenchmark
% 0.22/0.41 % SZS output start Proof for theBenchmark
% 0.22/0.41 thf(type_def_5, type, mworld: $tType).
% 0.22/0.41 thf(func_def_0, type, mworld: $tType).
% 0.22/0.41 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 0.22/0.41 thf(func_def_2, type, mactual: mworld).
% 0.22/0.41 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 0.22/0.41 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 0.22/0.41 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.22/0.41 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.22/0.41 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.22/0.41 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.22/0.41 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 0.22/0.41 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 0.22/0.41 thf(func_def_12, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 0.22/0.41 thf(func_def_13, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 0.22/0.41 thf(func_def_17, type, h: $i > mworld > $o).
% 0.22/0.41 thf(func_def_18, type, closed: $i > mworld > $o).
% 0.22/0.41 thf(func_def_19, type, combo: $i > $i > mworld > $o).
% 0.22/0.41 thf(func_def_20, type, open: $i > mworld > $o).
% 0.22/0.41 thf(func_def_38, type, sK1: $i > mworld > $i > $i).
% 0.22/0.41 thf(func_def_39, type, sK2: mworld).
% 0.22/0.41 thf(func_def_40, type, sK3: mworld).
% 0.22/0.41 thf(f313,plain,(
% 0.22/0.41 $false),
% 0.22/0.41 inference(avatar_sat_refutation,[],[f208,f230,f271,f282,f300,f311])).
% 0.22/0.41 thf(f311,plain,(
% 0.22/0.41 ~spl0_6),
% 0.22/0.41 inference(avatar_contradiction_clause,[],[f310])).
% 0.22/0.41 thf(f310,plain,(
% 0.22/0.41 $false | ~spl0_6),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f305])).
% 0.22/0.41 thf(f305,plain,(
% 0.22/0.41 ($true = $false) | ~spl0_6),
% 0.22/0.41 inference(superposition,[],[f127,f252])).
% 0.22/0.41 thf(f252,plain,(
% 0.22/0.41 ((mrel @ mactual @ sK2) = $false) | ~spl0_6),
% 0.22/0.41 inference(avatar_component_clause,[],[f250])).
% 0.22/0.41 thf(f250,plain,(
% 0.22/0.41 spl0_6 <=> ((mrel @ mactual @ sK2) = $false)),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl0_6])])).
% 0.22/0.41 thf(f127,plain,(
% 0.22/0.41 ((mrel @ mactual @ sK2) = $true)),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f125])).
% 0.22/0.41 thf(f125,plain,(
% 0.22/0.41 ($false = ((mrel @ mactual @ sK2) => (?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK2 @ Y2) => ((combo @ d @ Y0 @ Y2) & (h @ Y1 @ Y2))))) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK2 @ Y2) => (open @ d @ Y2)))))))))))),
% 0.22/0.41 inference(beta_eta_normalization,[],[f124])).
% 0.22/0.41 thf(f124,plain,(
% 0.22/0.41 (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y3) => ((combo @ d @ Y1 @ Y3) & (h @ Y2 @ Y3))))) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y3) => (open @ d @ Y3))))))))))) @ sK2) = $false)),
% 0.22/0.41 inference(sigma_clausification,[],[f123])).
% 0.22/0.41 thf(f123,plain,(
% 0.22/0.41 ($true != (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y3) => ((combo @ d @ Y1 @ Y3) & (h @ Y2 @ Y3))))) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y3) => (open @ d @ Y3)))))))))))))),
% 0.22/0.41 inference(beta_eta_normalization,[],[f77])).
% 0.22/0.41 thf(f77,plain,(
% 0.22/0.41 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (?? @ $i @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : $i]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) => (Y3 @ Y4))))))) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld]: (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) & (Y3 @ Y4))))))) @ (combo @ d @ Y0) @ (h @ Y1))) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld]: (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ (open @ d))))))))) != $true)),
% 0.22/0.41 inference(definition_unfolding,[],[f64,f62,f59,f65,f65,f61,f59,f74,f59])).
% 0.22/0.41 thf(f74,plain,(
% 0.22/0.41 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 0.22/0.41 inference(cnf_transformation,[],[f22])).
% 0.22/0.41 thf(f22,plain,(
% 0.22/0.41 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 0.22/0.41 inference(fool_elimination,[],[f21])).
% 0.22/0.41 thf(f21,plain,(
% 0.22/0.41 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X0 @ X2))) = mand)),
% 0.22/0.41 inference(rectify,[],[f3])).
% 0.22/0.41 thf(f3,axiom,(
% 0.22/0.41 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) & (X1 @ X2))) = mand)),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand_def)).
% 0.22/0.41 thf(f61,plain,(
% 0.22/0.41 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.22/0.41 inference(cnf_transformation,[],[f53])).
% 0.22/0.41 thf(f53,plain,(
% 0.22/0.41 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.22/0.41 inference(fool_elimination,[],[f52])).
% 0.22/0.41 thf(f52,plain,(
% 0.22/0.41 (mimplies = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 0.22/0.41 inference(rectify,[],[f5])).
% 0.22/0.41 thf(f5,axiom,(
% 0.22/0.41 (mimplies = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))))),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies_def)).
% 0.22/0.41 thf(f65,plain,(
% 0.22/0.41 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.22/0.41 inference(cnf_transformation,[],[f30])).
% 0.22/0.41 thf(f30,plain,(
% 0.22/0.41 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.22/0.41 inference(fool_elimination,[],[f29])).
% 0.22/0.41 thf(f29,plain,(
% 0.22/0.41 ((^[X0 : $i > mworld > $o, X1 : mworld] : (? [X2] : (X0 @ X2 @ X1))) = mexists_di)),
% 0.22/0.41 inference(rectify,[],[f12])).
% 0.22/0.41 thf(f12,axiom,(
% 0.22/0.41 ((^[X1 : $i > mworld > $o, X2 : mworld] : (? [X6] : (X1 @ X6 @ X2))) = mexists_di)),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_di_def)).
% 0.22/0.41 thf(f59,plain,(
% 0.22/0.41 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.22/0.41 inference(cnf_transformation,[],[f44])).
% 0.22/0.41 thf(f44,plain,(
% 0.22/0.41 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.22/0.41 inference(fool_elimination,[],[f43])).
% 0.22/0.41 thf(f43,plain,(
% 0.22/0.41 ((^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))) = mbox)),
% 0.22/0.41 inference(rectify,[],[f7])).
% 0.22/0.41 thf(f7,axiom,(
% 0.22/0.41 ((^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))) = mbox)),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_def)).
% 0.22/0.41 thf(f62,plain,(
% 0.22/0.41 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.22/0.41 inference(cnf_transformation,[],[f45])).
% 0.22/0.41 thf(f45,plain,(
% 0.22/0.41 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.22/0.41 inference(fool_elimination,[],[f1])).
% 0.22/0.41 thf(f1,axiom,(
% 0.22/0.41 (mlocal = (^[X0 : mworld > $o] : (X0 @ mactual)))),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def)).
% 0.22/0.41 thf(f64,plain,(
% 0.22/0.41 ($true != (mlocal @ (mbox @ (mexists_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mimplies @ (mbox @ (mand @ (combo @ d @ Y0) @ (h @ Y1))) @ (mbox @ (open @ d))))))))))),
% 0.22/0.41 inference(cnf_transformation,[],[f56])).
% 0.22/0.41 thf(f56,plain,(
% 0.22/0.41 ($true != (mlocal @ (mbox @ (mexists_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mimplies @ (mbox @ (mand @ (combo @ d @ Y0) @ (h @ Y1))) @ (mbox @ (open @ d))))))))))),
% 0.22/0.41 inference(flattening,[],[f38])).
% 0.22/0.41 thf(f38,plain,(
% 0.22/0.41 ~($true = (mlocal @ (mbox @ (mexists_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mimplies @ (mbox @ (mand @ (combo @ d @ Y0) @ (h @ Y1))) @ (mbox @ (open @ d))))))))))),
% 0.22/0.41 inference(fool_elimination,[],[f37])).
% 0.22/0.41 thf(f37,plain,(
% 0.22/0.41 ~(mlocal @ (mbox @ (mexists_di @ (^[X0 : $i] : (mexists_di @ (^[X1 : $i] : (mimplies @ (mbox @ (mand @ (combo @ d @ X0) @ (h @ X1))) @ (mbox @ (open @ d)))))))))),
% 0.22/0.41 inference(rectify,[],[f19])).
% 0.22/0.41 thf(f19,negated_conjecture,(
% 0.22/0.41 ~(mlocal @ (mbox @ (mexists_di @ (^[X4 : $i] : (mexists_di @ (^[X8 : $i] : (mimplies @ (mbox @ (mand @ (combo @ d @ X4) @ (h @ X8))) @ (mbox @ (open @ d)))))))))),
% 0.22/0.41 inference(negated_conjecture,[],[f18])).
% 0.22/0.41 thf(f18,conjecture,(
% 0.22/0.41 (mlocal @ (mbox @ (mexists_di @ (^[X4 : $i] : (mexists_di @ (^[X8 : $i] : (mimplies @ (mbox @ (mand @ (combo @ d @ X4) @ (h @ X8))) @ (mbox @ (open @ d)))))))))),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',con)).
% 0.22/0.41 thf(f300,plain,(
% 0.22/0.41 ~spl0_7),
% 0.22/0.41 inference(avatar_contradiction_clause,[],[f299])).
% 0.22/0.41 thf(f299,plain,(
% 0.22/0.41 $false | ~spl0_7),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f293])).
% 0.22/0.41 thf(f293,plain,(
% 0.22/0.41 ($true = $false) | ~spl0_7),
% 0.22/0.41 inference(superposition,[],[f292,f142])).
% 0.22/0.41 thf(f142,plain,(
% 0.22/0.41 ((mrel @ sK2 @ sK3) = $true)),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f140])).
% 0.22/0.41 thf(f140,plain,(
% 0.22/0.41 (((mrel @ sK2 @ sK3) => (open @ d @ sK3)) = $false)),
% 0.22/0.41 inference(beta_eta_normalization,[],[f139])).
% 0.22/0.41 thf(f139,plain,(
% 0.22/0.41 (((^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => (open @ d @ Y0))) @ sK3) = $false)),
% 0.22/0.41 inference(sigma_clausification,[],[f132])).
% 0.22/0.41 thf(f132,plain,(
% 0.22/0.41 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => (open @ d @ Y0)))) = $false)),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f131])).
% 0.22/0.41 thf(f131,plain,(
% 0.22/0.41 ( ! [X2 : $i,X1 : $i] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => ((combo @ d @ X1 @ Y0) & (h @ X2 @ Y0))))) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => (open @ d @ Y0))))) = $false)) )),
% 0.22/0.41 inference(beta_eta_normalization,[],[f130])).
% 0.22/0.41 thf(f130,plain,(
% 0.22/0.41 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK2 @ Y1) => ((combo @ d @ X1 @ Y1) & (h @ Y0 @ Y1))))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK2 @ Y1) => (open @ d @ Y1)))))) @ X2) = $false)) )),
% 0.22/0.41 inference(pi_clausification,[],[f129])).
% 0.22/0.41 thf(f129,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (((?? @ $i @ (^[Y0 : $i]: ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK2 @ Y1) => ((combo @ d @ X1 @ Y1) & (h @ Y0 @ Y1))))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK2 @ Y1) => (open @ d @ Y1))))))) = $false)) )),
% 0.22/0.41 inference(beta_eta_normalization,[],[f128])).
% 0.22/0.41 thf(f128,plain,(
% 0.22/0.41 ( ! [X1 : $i] : ((((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK2 @ Y2) => ((combo @ d @ Y0 @ Y2) & (h @ Y1 @ Y2))))) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK2 @ Y2) => (open @ d @ Y2)))))))) @ X1) = $false)) )),
% 0.22/0.41 inference(pi_clausification,[],[f126])).
% 0.22/0.41 thf(f126,plain,(
% 0.22/0.41 ((?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK2 @ Y2) => ((combo @ d @ Y0 @ Y2) & (h @ Y1 @ Y2))))) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK2 @ Y2) => (open @ d @ Y2))))))))) = $false)),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f125])).
% 0.22/0.41 thf(f292,plain,(
% 0.22/0.41 ((mrel @ sK2 @ sK3) = $false) | ~spl0_7),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f285])).
% 0.22/0.41 thf(f285,plain,(
% 0.22/0.41 ($true = $false) | ((mrel @ sK2 @ sK3) = $false) | ~spl0_7),
% 0.22/0.41 inference(superposition,[],[f255,f141])).
% 0.22/0.41 thf(f141,plain,(
% 0.22/0.41 ((open @ d @ sK3) = $false)),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f140])).
% 0.22/0.41 thf(f255,plain,(
% 0.22/0.41 ( ! [X0 : mworld] : (($true = (open @ d @ X0)) | ((mrel @ sK2 @ X0) = $false)) ) | ~spl0_7),
% 0.22/0.41 inference(avatar_component_clause,[],[f254])).
% 0.22/0.41 thf(f254,plain,(
% 0.22/0.41 spl0_7 <=> ! [X0 : mworld] : (((mrel @ sK2 @ X0) = $false) | ($true = (open @ d @ X0)))),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl0_7])])).
% 0.22/0.41 thf(f282,plain,(
% 0.22/0.41 ~spl0_5),
% 0.22/0.41 inference(avatar_contradiction_clause,[],[f281])).
% 0.22/0.41 thf(f281,plain,(
% 0.22/0.41 $false | ~spl0_5),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f275])).
% 0.22/0.41 thf(f275,plain,(
% 0.22/0.41 ($true = $false) | ~spl0_5),
% 0.22/0.41 inference(superposition,[],[f162,f248])).
% 0.22/0.41 thf(f248,plain,(
% 0.22/0.41 ((closed @ d @ sK2) = $false) | ~spl0_5),
% 0.22/0.41 inference(avatar_component_clause,[],[f246])).
% 0.22/0.41 thf(f246,plain,(
% 0.22/0.41 spl0_5 <=> ((closed @ d @ sK2) = $false)),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl0_5])])).
% 0.22/0.41 thf(f162,plain,(
% 0.22/0.41 ((closed @ d @ sK2) = $true)),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f157])).
% 0.22/0.41 thf(f157,plain,(
% 0.22/0.41 ($true = $false) | ((closed @ d @ sK2) = $true)),
% 0.22/0.41 inference(superposition,[],[f117,f127])).
% 0.22/0.41 thf(f117,plain,(
% 0.22/0.41 ( ! [X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ((closed @ d @ X1) = $true)) )),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f116])).
% 0.22/0.41 thf(f116,plain,(
% 0.22/0.41 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => (closed @ d @ X1)))) )),
% 0.22/0.41 inference(beta_eta_normalization,[],[f115])).
% 0.22/0.41 thf(f115,plain,(
% 0.22/0.41 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (closed @ d @ Y0))) @ X1) = $true)) )),
% 0.22/0.41 inference(pi_clausification,[],[f114])).
% 0.22/0.41 thf(f114,plain,(
% 0.22/0.41 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (closed @ d @ Y0)))))),
% 0.22/0.41 inference(beta_eta_normalization,[],[f79])).
% 0.22/0.41 thf(f79,plain,(
% 0.22/0.41 ($true = ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (closed @ d))))),
% 0.22/0.41 inference(definition_unfolding,[],[f67,f62,f59])).
% 0.22/0.41 thf(f67,plain,(
% 0.22/0.41 ((mlocal @ (mbox @ (closed @ d))) = $true)),
% 0.22/0.41 inference(cnf_transformation,[],[f40])).
% 0.22/0.41 thf(f40,plain,(
% 0.22/0.41 ((mlocal @ (mbox @ (closed @ d))) = $true)),
% 0.22/0.41 inference(fool_elimination,[],[f39])).
% 0.22/0.41 thf(f39,plain,(
% 0.22/0.41 (mlocal @ (mbox @ (closed @ d)))),
% 0.22/0.41 inference(rectify,[],[f14])).
% 0.22/0.41 thf(f14,axiom,(
% 0.22/0.41 (mlocal @ (mbox @ (closed @ d)))),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2)).
% 0.22/0.41 thf(f271,plain,(
% 0.22/0.41 spl0_5 | spl0_6 | spl0_7 | ~spl0_1),
% 0.22/0.41 inference(avatar_split_clause,[],[f238,f194,f254,f250,f246])).
% 0.22/0.41 thf(f194,plain,(
% 0.22/0.41 spl0_1 <=> ! [X2,X0,X3 : mworld] : (($false = (combo @ X2 @ X0 @ sK2)) | ((closed @ X2 @ sK2) = $false) | ((mrel @ sK2 @ X3) = $false) | ($true = (open @ X2 @ X3)))),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.22/0.41 thf(f238,plain,(
% 0.22/0.41 ( ! [X0 : mworld] : (((mrel @ mactual @ sK2) = $false) | ($true = (open @ d @ X0)) | ((closed @ d @ sK2) = $false) | ((mrel @ sK2 @ X0) = $false)) ) | ~spl0_1),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f236])).
% 0.22/0.41 thf(f236,plain,(
% 0.22/0.41 ( ! [X0 : mworld] : (($true = $false) | ($true = (open @ d @ X0)) | ((closed @ d @ sK2) = $false) | ((mrel @ mactual @ sK2) = $false) | ((mrel @ sK2 @ X0) = $false)) ) | ~spl0_1),
% 0.22/0.41 inference(superposition,[],[f148,f195])).
% 0.22/0.41 thf(f195,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : mworld,X0 : $i] : (($false = (combo @ X2 @ X0 @ sK2)) | ((mrel @ sK2 @ X3) = $false) | ((closed @ X2 @ sK2) = $false) | ($true = (open @ X2 @ X3))) ) | ~spl0_1),
% 0.22/0.41 inference(avatar_component_clause,[],[f194])).
% 0.22/0.41 thf(f148,plain,(
% 0.22/0.41 ( ! [X1 : mworld] : (((combo @ d @ sK4 @ X1) = $true) | ((mrel @ mactual @ X1) = $false)) )),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f147])).
% 0.22/0.41 thf(f147,plain,(
% 0.22/0.41 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1) => (combo @ d @ sK4 @ X1)) = $true)) )),
% 0.22/0.41 inference(beta_eta_normalization,[],[f146])).
% 0.22/0.41 thf(f146,plain,(
% 0.22/0.41 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (combo @ d @ sK4 @ Y0))) @ X1) = $true)) )),
% 0.22/0.41 inference(pi_clausification,[],[f145])).
% 0.22/0.41 thf(f145,plain,(
% 0.22/0.41 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (combo @ d @ sK4 @ Y0)))) = $true)),
% 0.22/0.41 inference(beta_eta_normalization,[],[f144])).
% 0.22/0.41 thf(f144,plain,(
% 0.22/0.41 (((^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ mactual @ Y1) => (combo @ d @ Y0 @ Y1))))) @ sK4) = $true)),
% 0.22/0.41 inference(sigma_clausification,[],[f143])).
% 0.22/0.41 thf(f143,plain,(
% 0.22/0.41 ((?? @ $i @ (^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ mactual @ Y1) => (combo @ d @ Y0 @ Y1)))))) = $true)),
% 0.22/0.41 inference(beta_eta_normalization,[],[f78])).
% 0.22/0.41 thf(f78,plain,(
% 0.22/0.41 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (Y1 @ Y3))))))) @ (combo @ d @ Y0))))) = $true)),
% 0.22/0.41 inference(definition_unfolding,[],[f66,f62,f65,f59])).
% 0.22/0.41 thf(f66,plain,(
% 0.22/0.41 ((mlocal @ (mexists_di @ (^[Y0 : $i]: (mbox @ (combo @ d @ Y0))))) = $true)),
% 0.22/0.41 inference(cnf_transformation,[],[f51])).
% 0.22/0.41 thf(f51,plain,(
% 0.22/0.41 ((mlocal @ (mexists_di @ (^[Y0 : $i]: (mbox @ (combo @ d @ Y0))))) = $true)),
% 0.22/0.41 inference(fool_elimination,[],[f50])).
% 0.22/0.41 thf(f50,plain,(
% 0.22/0.41 (mlocal @ (mexists_di @ (^[X0 : $i] : (mbox @ (combo @ d @ X0)))))),
% 0.22/0.41 inference(rectify,[],[f17])).
% 0.22/0.41 thf(f17,axiom,(
% 0.22/0.41 (mlocal @ (mexists_di @ (^[X4 : $i] : (mbox @ (combo @ d @ X4)))))),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5)).
% 0.22/0.41 thf(f230,plain,(
% 0.22/0.41 ~spl0_2),
% 0.22/0.41 inference(avatar_contradiction_clause,[],[f229])).
% 0.22/0.41 thf(f229,plain,(
% 0.22/0.41 $false | ~spl0_2),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f221])).
% 0.22/0.41 thf(f221,plain,(
% 0.22/0.41 ($true = $false) | ~spl0_2),
% 0.22/0.41 inference(superposition,[],[f217,f127])).
% 0.22/0.41 thf(f217,plain,(
% 0.22/0.41 ((mrel @ mactual @ sK2) = $false) | ~spl0_2),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f210])).
% 0.22/0.41 thf(f210,plain,(
% 0.22/0.41 ($true = $false) | ((mrel @ mactual @ sK2) = $false) | ~spl0_2),
% 0.22/0.41 inference(superposition,[],[f198,f60])).
% 0.22/0.41 thf(f60,plain,(
% 0.22/0.41 ( ! [X0 : mworld] : (($true = (mrel @ X0 @ X0))) )),
% 0.22/0.41 inference(cnf_transformation,[],[f49])).
% 0.22/0.41 thf(f49,plain,(
% 0.22/0.41 ! [X0 : mworld] : ($true = (mrel @ X0 @ X0))),
% 0.22/0.41 inference(fool_elimination,[],[f48])).
% 0.22/0.41 thf(f48,plain,(
% 0.22/0.41 ! [X0 : mworld] : (mrel @ X0 @ X0)),
% 0.22/0.41 inference(rectify,[],[f9])).
% 0.22/0.41 thf(f9,axiom,(
% 0.22/0.41 ! [X2 : mworld] : (mrel @ X2 @ X2)),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive)).
% 0.22/0.41 thf(f198,plain,(
% 0.22/0.41 ( ! [X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ((mrel @ X1 @ sK2) = $false)) ) | ~spl0_2),
% 0.22/0.41 inference(avatar_component_clause,[],[f197])).
% 0.22/0.41 thf(f197,plain,(
% 0.22/0.41 spl0_2 <=> ! [X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ((mrel @ X1 @ sK2) = $false))),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.22/0.41 thf(f208,plain,(
% 0.22/0.41 spl0_2 | spl0_1),
% 0.22/0.41 inference(avatar_split_clause,[],[f187,f194,f197])).
% 0.22/0.41 thf(f187,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : mworld,X0 : $i,X1 : mworld] : (((mrel @ sK2 @ X3) = $false) | ((mrel @ X1 @ sK2) = $false) | ((closed @ X2 @ sK2) = $false) | ($true = (open @ X2 @ X3)) | ($false = (combo @ X2 @ X0 @ sK2)) | ((mrel @ mactual @ X1) = $false)) )),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f184])).
% 0.22/0.41 thf(f184,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : mworld,X0 : $i,X1 : mworld] : (($false = (combo @ X2 @ X0 @ sK2)) | ($true = $false) | ((mrel @ X1 @ sK2) = $false) | ((mrel @ sK2 @ X3) = $false) | ($true = (open @ X2 @ X3)) | ((closed @ X2 @ sK2) = $false) | ((mrel @ mactual @ X1) = $false)) )),
% 0.22/0.41 inference(superposition,[],[f171,f103])).
% 0.22/0.41 thf(f103,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : mworld,X5 : mworld] : (((h @ (sK1 @ X3 @ X1 @ X2) @ X4) = $false) | ((combo @ X2 @ X3 @ X4) = $false) | ((closed @ X2 @ X4) = $false) | ($true = (open @ X2 @ X5)) | ((mrel @ X4 @ X5) = $false) | ((mrel @ mactual @ X1) = $false) | ((mrel @ X1 @ X4) = $false)) )),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f102])).
% 0.22/0.41 thf(f102,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : mworld,X5 : mworld] : (((mrel @ X1 @ X4) = $false) | ($true = ((mrel @ X4 @ X5) => (open @ X2 @ X5))) | ((closed @ X2 @ X4) = $false) | ((combo @ X2 @ X3 @ X4) = $false) | ((mrel @ mactual @ X1) = $false) | ((h @ (sK1 @ X3 @ X1 @ X2) @ X4) = $false)) )),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f101])).
% 0.22/0.41 thf(f101,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : mworld,X5 : mworld] : (((mrel @ X1 @ X4) = $false) | (((combo @ X2 @ X3 @ X4) & (h @ (sK1 @ X3 @ X1 @ X2) @ X4)) = $false) | ($true = ((mrel @ X4 @ X5) => (open @ X2 @ X5))) | ((closed @ X2 @ X4) = $false) | ((mrel @ mactual @ X1) = $false)) )),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f100])).
% 0.22/0.41 thf(f100,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : mworld,X5 : mworld] : (((mrel @ X1 @ X4) = $false) | (((closed @ X2 @ X4) & ((combo @ X2 @ X3 @ X4) & (h @ (sK1 @ X3 @ X1 @ X2) @ X4))) = $false) | ((mrel @ mactual @ X1) = $false) | ($true = ((mrel @ X4 @ X5) => (open @ X2 @ X5)))) )),
% 0.22/0.41 inference(beta_eta_normalization,[],[f99])).
% 0.22/0.41 thf(f99,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : mworld,X5 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (open @ X2 @ Y0))) @ X5) = $true) | ((mrel @ X1 @ X4) = $false) | (((closed @ X2 @ X4) & ((combo @ X2 @ X3 @ X4) & (h @ (sK1 @ X3 @ X1 @ X2) @ X4))) = $false) | ((mrel @ mactual @ X1) = $false)) )),
% 0.22/0.41 inference(pi_clausification,[],[f98])).
% 0.22/0.41 thf(f98,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : mworld] : (((mrel @ mactual @ X1) = $false) | ((mrel @ X1 @ X4) = $false) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (open @ X2 @ Y0)))) = $true) | (((closed @ X2 @ X4) & ((combo @ X2 @ X3 @ X4) & (h @ (sK1 @ X3 @ X1 @ X2) @ X4))) = $false)) )),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f97])).
% 0.22/0.41 thf(f97,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : mworld] : (((mrel @ X1 @ X4) = $false) | ((mrel @ mactual @ X1) = $false) | ((((closed @ X2 @ X4) & ((combo @ X2 @ X3 @ X4) & (h @ (sK1 @ X3 @ X1 @ X2) @ X4))) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (open @ X2 @ Y0))))) = $true)) )),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f96])).
% 0.22/0.41 thf(f96,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : mworld] : (((mrel @ mactual @ X1) = $false) | ($true = ((mrel @ X1 @ X4) => (((closed @ X2 @ X4) & ((combo @ X2 @ X3 @ X4) & (h @ (sK1 @ X3 @ X1 @ X2) @ X4))) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (open @ X2 @ Y0)))))))) )),
% 0.22/0.41 inference(beta_eta_normalization,[],[f95])).
% 0.22/0.41 thf(f95,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : mworld] : (((mrel @ mactual @ X1) = $false) | ($true = ((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (((closed @ X2 @ Y0) & ((combo @ X2 @ X3 @ Y0) & (h @ (sK1 @ X3 @ X1 @ X2) @ Y0))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (open @ X2 @ Y1))))))) @ X4))) )),
% 0.22/0.41 inference(pi_clausification,[],[f94])).
% 0.22/0.41 thf(f94,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i,X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (((closed @ X2 @ Y0) & ((combo @ X2 @ X3 @ Y0) & (h @ (sK1 @ X3 @ X1 @ X2) @ Y0))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (open @ X2 @ Y1)))))))) = $true)) )),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f92])).
% 0.22/0.41 thf(f92,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i,X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (((closed @ X2 @ Y0) & ((combo @ X2 @ X3 @ Y0) & (h @ (sK1 @ X3 @ X1 @ X2) @ Y0))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (open @ X2 @ Y1)))))))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (((closed @ X2 @ Y0) & ((~ (combo @ X2 @ X3 @ Y0)) & (h @ o @ Y0))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (closed @ X2 @ Y1))))))))))) )),
% 0.22/0.41 inference(beta_eta_normalization,[],[f91])).
% 0.22/0.41 thf(f91,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i,X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ($true = ((^[Y0 : $i]: ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (((closed @ X2 @ Y1) & ((combo @ X2 @ X3 @ Y1) & (h @ Y0 @ Y1))) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (open @ X2 @ Y2)))))))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (((closed @ X2 @ Y1) & ((~ (combo @ X2 @ X3 @ Y1)) & (h @ o @ Y1))) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (closed @ X2 @ Y2)))))))))) @ (sK1 @ X3 @ X1 @ X2)))) )),
% 0.22/0.41 inference(sigma_clausification,[],[f90])).
% 0.22/0.41 thf(f90,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i,X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ((?? @ $i @ (^[Y0 : $i]: ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (((closed @ X2 @ Y1) & ((combo @ X2 @ X3 @ Y1) & (h @ Y0 @ Y1))) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (open @ X2 @ Y2)))))))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (((closed @ X2 @ Y1) & ((~ (combo @ X2 @ X3 @ Y1)) & (h @ o @ Y1))) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (closed @ X2 @ Y2))))))))))) = $true)) )),
% 0.22/0.41 inference(beta_eta_normalization,[],[f89])).
% 0.22/0.41 thf(f89,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i,X1 : mworld] : (((mrel @ mactual @ X1) = $false) | (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (((closed @ X2 @ Y2) & ((combo @ X2 @ Y0 @ Y2) & (h @ Y1 @ Y2))) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (open @ X2 @ Y3)))))))) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (((closed @ X2 @ Y2) & ((~ (combo @ X2 @ Y0 @ Y2)) & (h @ o @ Y2))) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (closed @ X2 @ Y3)))))))))))) @ X3) = $true)) )),
% 0.22/0.41 inference(pi_clausification,[],[f88])).
% 0.22/0.41 thf(f88,plain,(
% 0.22/0.41 ( ! [X2 : $i,X1 : mworld] : (($true = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (((closed @ X2 @ Y2) & ((combo @ X2 @ Y0 @ Y2) & (h @ Y1 @ Y2))) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (open @ X2 @ Y3)))))))) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (((closed @ X2 @ Y2) & ((~ (combo @ X2 @ Y0 @ Y2)) & (h @ o @ Y2))) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (closed @ X2 @ Y3)))))))))))))) | ((mrel @ mactual @ X1) = $false)) )),
% 0.22/0.41 inference(beta_eta_normalization,[],[f87])).
% 0.22/0.41 thf(f87,plain,(
% 0.22/0.41 ( ! [X2 : $i,X1 : mworld] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ X1 @ Y3) => (((closed @ Y0 @ Y3) & ((combo @ Y0 @ Y1 @ Y3) & (h @ Y2 @ Y3))) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (open @ Y0 @ Y4)))))))) & (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ X1 @ Y3) => (((closed @ Y0 @ Y3) & ((~ (combo @ Y0 @ Y1 @ Y3)) & (h @ o @ Y3))) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (closed @ Y0 @ Y4)))))))))))))) @ X2) = $true) | ((mrel @ mactual @ X1) = $false)) )),
% 0.22/0.41 inference(pi_clausification,[],[f86])).
% 0.22/0.41 thf(f86,plain,(
% 0.22/0.41 ( ! [X1 : mworld] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ X1 @ Y3) => (((closed @ Y0 @ Y3) & ((combo @ Y0 @ Y1 @ Y3) & (h @ Y2 @ Y3))) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (open @ Y0 @ Y4)))))))) & (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ X1 @ Y3) => (((closed @ Y0 @ Y3) & ((~ (combo @ Y0 @ Y1 @ Y3)) & (h @ o @ Y3))) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (closed @ Y0 @ Y4))))))))))))))) = $true) | ((mrel @ mactual @ X1) = $false)) )),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f85])).
% 0.22/0.41 thf(f85,plain,(
% 0.22/0.41 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ X1 @ Y3) => (((closed @ Y0 @ Y3) & ((combo @ Y0 @ Y1 @ Y3) & (h @ Y2 @ Y3))) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (open @ Y0 @ Y4)))))))) & (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ X1 @ Y3) => (((closed @ Y0 @ Y3) & ((~ (combo @ Y0 @ Y1 @ Y3)) & (h @ o @ Y3))) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (closed @ Y0 @ Y4)))))))))))))))) = $true)) )),
% 0.22/0.41 inference(beta_eta_normalization,[],[f84])).
% 0.22/0.41 thf(f84,plain,(
% 0.22/0.41 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y0 @ Y4) => (((closed @ Y1 @ Y4) & ((combo @ Y1 @ Y2 @ Y4) & (h @ Y3 @ Y4))) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (open @ Y1 @ Y5)))))))) & (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y0 @ Y4) => (((closed @ Y1 @ Y4) & ((~ (combo @ Y1 @ Y2 @ Y4)) & (h @ o @ Y4))) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (closed @ Y1 @ Y5))))))))))))))))) @ X1))) )),
% 0.22/0.41 inference(pi_clausification,[],[f83])).
% 0.22/0.41 thf(f83,plain,(
% 0.22/0.41 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y0 @ Y4) => (((closed @ Y1 @ Y4) & ((combo @ Y1 @ Y2 @ Y4) & (h @ Y3 @ Y4))) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (open @ Y1 @ Y5)))))))) & (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y0 @ Y4) => (((closed @ Y1 @ Y4) & ((~ (combo @ Y1 @ Y2 @ Y4)) & (h @ o @ Y4))) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (closed @ Y1 @ Y5)))))))))))))))))) = $true)),
% 0.22/0.41 inference(beta_eta_normalization,[],[f81])).
% 0.22/0.41 thf(f81,plain,(
% 0.22/0.41 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (!! @ $i @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : $i]: ((^[Y2 : $i > mworld > $o]: ((^[Y3 : mworld]: (?? @ $i @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : $i]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) & (Y4 @ Y5))))))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (Y3 @ Y5))))))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) => (Y4 @ Y5))))))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) & (Y4 @ Y5))))))) @ (closed @ Y0) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) & (Y4 @ Y5))))))) @ (combo @ Y0 @ Y1) @ (h @ Y2))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (Y3 @ Y5))))))) @ (open @ Y0)))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (Y3 @ Y5))))))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) => (Y4 @ Y5))))))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) & (Y4 @ Y5))))))) @ (closed @ Y0) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) & (Y4 @ Y5))))))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: (~ (Y3 @ Y4))))) @ (combo @ Y0 @ Y1)) @ (h @ o))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (Y3 @ Y5))))))) @ (closed @ Y0))))))))))))) = $true)),
% 0.22/0.41 inference(definition_unfolding,[],[f70,f62,f59,f76,f76,f65,f74,f59,f61,f74,f74,f59,f59,f61,f74,f74,f69,f59])).
% 0.22/0.41 thf(f69,plain,(
% 0.22/0.41 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 0.22/0.41 inference(cnf_transformation,[],[f36])).
% 0.22/0.41 thf(f36,plain,(
% 0.22/0.41 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 0.22/0.41 inference(fool_elimination,[],[f35])).
% 0.22/0.41 thf(f35,plain,(
% 0.22/0.41 ((^[X0 : mworld > $o, X1 : mworld] : (~(X0 @ X1))) = mnot)),
% 0.22/0.41 inference(rectify,[],[f2])).
% 0.22/0.41 thf(f2,axiom,(
% 0.22/0.41 ((^[X1 : mworld > $o, X2 : mworld] : (~(X1 @ X2))) = mnot)),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot_def)).
% 0.22/0.41 thf(f76,plain,(
% 0.22/0.41 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.22/0.41 inference(cnf_transformation,[],[f34])).
% 0.22/0.41 thf(f34,plain,(
% 0.22/0.41 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.22/0.41 inference(fool_elimination,[],[f33])).
% 0.22/0.41 thf(f33,plain,(
% 0.22/0.41 (mforall_di = (^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2] : (X0 @ X2 @ X1))))),
% 0.22/0.41 inference(rectify,[],[f11])).
% 0.22/0.41 thf(f11,axiom,(
% 0.22/0.41 (mforall_di = (^[X1 : $i > mworld > $o, X2 : mworld] : (! [X6] : (X1 @ X6 @ X2))))),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_di_def)).
% 0.22/0.41 thf(f70,plain,(
% 0.22/0.41 ((mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mexists_di @ (^[Y2 : $i]: (mand @ (mbox @ (mimplies @ (mand @ (closed @ Y0) @ (mand @ (combo @ Y0 @ Y1) @ (h @ Y2))) @ (mbox @ (open @ Y0)))) @ (mbox @ (mimplies @ (mand @ (closed @ Y0) @ (mand @ (mnot @ (combo @ Y0 @ Y1)) @ (h @ o))) @ (mbox @ (closed @ Y0))))))))))))) = $true)),
% 0.22/0.41 inference(cnf_transformation,[],[f47])).
% 0.22/0.41 thf(f47,plain,(
% 0.22/0.41 ((mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mexists_di @ (^[Y2 : $i]: (mand @ (mbox @ (mimplies @ (mand @ (closed @ Y0) @ (mand @ (combo @ Y0 @ Y1) @ (h @ Y2))) @ (mbox @ (open @ Y0)))) @ (mbox @ (mimplies @ (mand @ (closed @ Y0) @ (mand @ (mnot @ (combo @ Y0 @ Y1)) @ (h @ o))) @ (mbox @ (closed @ Y0))))))))))))) = $true)),
% 0.22/0.41 inference(fool_elimination,[],[f46])).
% 0.22/0.41 thf(f46,plain,(
% 0.22/0.41 (mlocal @ (mbox @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mexists_di @ (^[X2 : $i] : (mand @ (mbox @ (mimplies @ (mand @ (closed @ X0) @ (mand @ (combo @ X0 @ X1) @ (h @ X2))) @ (mbox @ (open @ X0)))) @ (mbox @ (mimplies @ (mand @ (closed @ X0) @ (mand @ (mnot @ (combo @ X0 @ X1)) @ (h @ o))) @ (mbox @ (closed @ X0)))))))))))))),
% 0.22/0.41 inference(rectify,[],[f13])).
% 0.22/0.41 thf(f13,axiom,(
% 0.22/0.41 (mlocal @ (mbox @ (mforall_di @ (^[X7 : $i] : (mforall_di @ (^[X4 : $i] : (mexists_di @ (^[X8 : $i] : (mand @ (mbox @ (mimplies @ (mand @ (closed @ X7) @ (mand @ (combo @ X7 @ X4) @ (h @ X8))) @ (mbox @ (open @ X7)))) @ (mbox @ (mimplies @ (mand @ (closed @ X7) @ (mand @ (mnot @ (combo @ X7 @ X4)) @ (h @ o))) @ (mbox @ (closed @ X7)))))))))))))),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1)).
% 0.22/0.41 thf(f171,plain,(
% 0.22/0.41 ( ! [X0 : $i] : (($true = (h @ X0 @ sK2))) )),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f166])).
% 0.22/0.41 thf(f166,plain,(
% 0.22/0.41 ( ! [X0 : $i] : (($true = $false) | ($true = (h @ X0 @ sK2))) )),
% 0.22/0.41 inference(superposition,[],[f137,f60])).
% 0.22/0.41 thf(f137,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : mworld] : (((mrel @ sK2 @ X3) = $false) | ((h @ X2 @ X3) = $true)) )),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f136])).
% 0.22/0.41 thf(f136,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : mworld,X1 : $i] : (((mrel @ sK2 @ X3) = $false) | (((combo @ d @ X1 @ X3) & (h @ X2 @ X3)) = $true)) )),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f135])).
% 0.22/0.41 thf(f135,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : mworld,X1 : $i] : ((((mrel @ sK2 @ X3) => ((combo @ d @ X1 @ X3) & (h @ X2 @ X3))) = $true)) )),
% 0.22/0.41 inference(beta_eta_normalization,[],[f134])).
% 0.22/0.41 thf(f134,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : mworld,X1 : $i] : ((((^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => ((combo @ d @ X1 @ Y0) & (h @ X2 @ Y0)))) @ X3) = $true)) )),
% 0.22/0.41 inference(pi_clausification,[],[f133])).
% 0.22/0.41 thf(f133,plain,(
% 0.22/0.41 ( ! [X2 : $i,X1 : $i] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => ((combo @ d @ X1 @ Y0) & (h @ X2 @ Y0))))) = $true)) )),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f131])).
% 0.22/0.41 % SZS output end Proof for theBenchmark
% 0.22/0.41 % (3073)------------------------------
% 0.22/0.41 % (3073)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (3073)Termination reason: Refutation
% 0.22/0.41
% 0.22/0.41 % (3073)Memory used [KB]: 5884
% 0.22/0.41 % (3073)Time elapsed: 0.030 s
% 0.22/0.41 % (3073)Instructions burned: 34 (million)
% 0.22/0.41 % (3073)------------------------------
% 0.22/0.41 % (3073)------------------------------
% 0.22/0.41 % (3072)Success in time 0.05 s
% 0.22/0.41 % Vampire---4.8 exiting
%------------------------------------------------------------------------------